00:01
Today we're going to find and sketch the gradient of f of xy equals x squared minus y.
00:08
I'm calling the gradient nabler of f, standard vector calculus notation.
00:13
This stands for dx of f, where dx is the x derivative and d y of f.
00:21
Now, since f is a simple polynomial, we can see that the x derivative will just give us a 2x, and the y derivative will give us a minus 1.
00:32
So we get 2x and minus 1.
00:34
Now we need to sketch this on a pair of axes, x, y.
00:45
Now we can note when x equals 0, a gradient is just 0 minus 1.
00:55
So on the entire y axis, we go down 1 no matter where we are.
01:06
The length stays the same.
01:08
And then what we notice is if we deviate slightly away from the y axis, if we deviate slightly to the right, so if x is some small dx, we find df is dx minus one.
01:30
So in fact, it goes right a tiny bit...